Quaternions and Quaternion Colour Constancy. Quaternions Quaternions … Are a member of...
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Quaternions andQuaternion Colour Constancy
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Quaternions Quaternions …
Are a member of hypercomplex numbers Are a generalization of complex numbers Has one real part and three imaginary parts
i.e. A RGB colour is represented by a pure
quaternion
kbjgirq
kajaiaaa 3210
1
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Quaternions
A picture of quaternions Quaternion axes in 4D space
Pure quaternion for colour
reali
kj
i
kj
Orthogonal in 4D
“pure” = zero real part
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Quaternion PCA
QPCA is a generalization of complex PCA
QPCA for dimension reduction Similar to PCA for real numbers Quaternion-valued Texture can be
described in low dim. space
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Quaternion PCA
Figure 13: QPCA based image compression. (a) –(d) are the reconstructed images with k(# of basis vectors)=3,16,50,255. Note that (d) is the perfect reconstruction of the original image
(a) (b) (c) (d)
Eg. QPCA For Image Compression Each row of the image is a input variable QPCA on all rows
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QPCA for Texture Feature Extraction
Training
QPCA
Image-specific quaternion texture basisSampled sub-windows
Surprisingly, need only the first basis texture element
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Feature Extraction Feature Deduction
Single quaternion
A texture patch
1st QPCA Basis texture element
magnitude
real layerred layer
green layerblue layer
T
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Classification
Textures By classifying their extracted quaternion
features Images based on content
By recognizing the class of textures they contain
Images based on illumination By identifying the kind of illuminations of
textures they contain
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Colour Texture Histogram
An image contains colour textures Colour Texture Histogram
It counts different colour textures Quaternion texture can be used to
build colour histogram An extension of colour histogram
when each pixel is consider as a texture
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Quaternion For Colour Constancy Colour Constancy
SVR uses colour histograms Colour Histogram
Contains colour information only Texture Histogram
Contains structural information only Colour Texture Histogram
Integrates both colour and structure info A new representation of images Can SVR do better by Colour Texture Histogram?
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K-Medians Clustering for Training Set Reduction
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Function Estimation Define a function(curve) that minimizes the energy
function controlled by all training data points
Use this function to estimate new data SVR, TPS
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Control Point Reduction
Problem Training set too large to fit into memory Long processing time
Reduce training set using k-medians Partition n control points into k clusters Keep k medians of these clusters Reduce n control points to k
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k-Medians k-medians clustering:
Given: N points (x1… xN) in a metric space Find k points C = {c1, c2, …, ck} that minimize
Σ d(xi, C) (the assignment distance)
• In the example above, only 4 control points are needed to define the curve
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k-Medians k-medians
Median as the best representative for each cluster
Less sensitive to outliers k can be determined based on memory and
training time requirement